Beware, Caesars in AC is using shaved dice

Quote: Wizard

In 100 flips you would expect a reversal of the previous result 50 times. I would imagine that fake results would have more such reversals, in an effort to appear random. Just off the top of my head, I'd suspect a number of reversals outside of 40 to 60 to be faked.

Wizard, I admire the hell out of you and your site and if you want I'll buy you dinner at a nice place of your choosing the next time I come to Las Vegas (probably early December; I have to lose some money before the IRS taxes it) to thank you; I think I'd enjoy your company. You have a clear command of P&S and, even better, a great ability to explain these things to the average person which I find remarkable and admirable in the extreme.

You write that in 100 flips we should expect a reversal of the previous result 50 times. Actually, if you calculate the probability of that happening you'll find it excruciatingly rare that such a thing would ever happen (you know that of course; I write that for some of the others following this). Reversals outside of 40 to 60? I dunno; maybe. But I didn't use that metric and didn't detect them that way; that would have taken too long. Ditto for me having the ability to do chi-square testing in my head (I can't do that; at least not quickly).

Really, you can go look this exercise up if you want (a common class exercise in Probability and Statistics; I didn't invent it). I don't detail the method only because I don't want word to get around and poison a new cohort of students. It works best on the uninitiated, and the exercise has the goal of proving to the students, at a gut-level, that they (and other humans) don't do a good job at generating random numbers as human beings (as opposed to using random generators like coin flips).

But as a clue: consider the time-limit here. 20 sheets with 100 symbols/sheet, and 2 minutes, max to eyeball them all. Less, really.

Why don't you just give it a try both ways: fake it, and then flip the coin 100 times (recording the results each time). Then take a look at the two sheets and see if you notice any difference that stands out between them. Clearly it will take you longer than a few minutes to notice the difference because you don't know the trick. In fact, considering your expertise, perhaps you should have someone else do the fake part for you. :)

Quote: AxelWolf

Quote: Wizard

In 100 flips you would expect a reversal of the previous result 50 times. I would imagine that fake results would have more such reversals, in an effort to appear random. Just off the top of my head, I'd suspect a number of reversals outside of 40 to 60 to be faked.

Not sure how many times he did this. I assume 98% of the students just made up fake results. Who wants to flip a coin 100 times especially when they can have a shot at fooling a teacher?

I'm surprised no one actually flipped "fake looking results"

I'm sure at least a few students lied and claimed they actually flipped the coin. So how does that affect the %100 accurate results?

I didn't keep count of the number of times I did this. I would guess 9 or 10 years, once/year (how long I taught this stuff until I decided to go into consulting full-time), so figure I saw maybe 200 pages of results. Probably more. But as I have mentioned, I didn't invent this exercise (I steal from the masters though).

Actually, it always surprised me how many actually flipped the coins. More than half. :) I always wondered if that would change if I had taught undergraduates instead of graduate students in computer science.

And yes, "fake looking results" could certainly occur. In such an unlikely case I would have happily pounced on that lucky break and used it as an excuse to launch into a lecture on a different aspect of things. But it never happened. It could. Unlikely though.

I doubt very much that any students lied at all, given the institutions involved, that I used graduate students, that we had draconian honor codes, and that if they wanted to cheat they would have done so for something a hell of a lot more important, considering that they had to do the work (one way or the other) anyway. But in any event, believe what you wish regarding my level of accuracy, and I admire your skepticism.

Quote: DRich

Why didn't you play the Don't. You would have made a fortune.

............. Sorry quoted the wrong person.

Quote: Thundershock

Because many times, the 7 was showing up on the first roll.

So the dice were shaved and they knew when the first roll was. Amazing!!!!!

If you were as smart as you think you are, then why didn't lay against any number on the come out. :-)